I thought it was Elizabeth who asked Prime Minister Eden to do it. I don’t think he did it on his own. Ironically, Eden had been divorced himself!
How times change!
I believe the original story was that it was the Queen Mum and Winston Churchill (and even Cabinet ministers!)who were the main players.
Here’s a version of the events:
https://www.theguardian.com/uk/2002/feb/09/monarchy.princessmargaret1